In this paper, a 1D stretchable terahertz (THz) metasurface based on laser-induced graphene (LIG) for deformation sensing is developed with low cost, good sensitivity and robustness. After the LIG metasurface is fabricated by laser-direct writing on a polyimide film, it is divided into columns and bonded to a medical polyurethane (PU) tape, thus endowed with high elasticity due to the excellent flexibility of PU. Because LIG supports surface plasmon polaritons in the THz band, a plasmonic resonance is introduced in the reflection spectrum and red shifts with lateral stretching. Experimental results show that the device can realize a resonant frequency shift of 336 GHz at a deformation of 0-14 mm, and the linearity reaches 0.988, achieving a sensitivity of 24 GHz/mm and excellent robustness (>1000 repetitions). The LIG-based stretchable THz sensor has great application potential for contactless deformation sensing in aerospace, industrial manufacturing, and related fields.